Posted by LILY on .
Is 14/3 a rational number? I think so... but I'm confused because if you divide 14 by 3 then the decimal part is .66666666666666666666667. Is that considered a repeating decimal? If it is, then it's a rational number. I'm just doubting because of the 7 at the end. THANKS SO MUCH!!! =D

math :] 2 
Reiny,
nothing to be confused about.
Your calculator has a buildin function which rounds off the last decimal it can display, that's why it shows up as a 7
When you do a long division, the way it was taught to you in earlier grades, the 6 will keep on repeating forever. 
math :] 2 
LILY,
So is it a national number or what?

math :] 2 
LILY,
I meant rational, so sorry.

math :] 2 
Reiny,
yes it is a rational number since it can be written as a fraction, or a RATIO.

math :] 2 
LILY,
thank you so muchhhhhhhh. =]

math :] 2 
Damon,
Ah, not to beat a dead horse here but let's make sure the cart is before that horse. The real point is that 14/3 is a RATIO of whole numbers as Reiny capitalized.
That is what makes it a rational number.
The fact that it is a repeating decimal means that it can be written as a ratio, and therefore is rational.
In other words
If ratio, then rational
If repeating decimal, then ratio
Therefore
If repeating decimal, then rational
I suspect shortly you will be shown how to find the ratio that corresponds to any repeating decimal.